Problem: $f(x)=2x+3$ $g(x)=x^2-3x+1$ Write $g(f(x))$ as an expression in terms of $x$. $g(f(x))=$
Explanation: Let's write $f(x)$ as the input to function $g$. $g({f(x)})=({f(x)})^2-3({f(x)})+1$ Since $f(x)=2x+3$, this becomes: $\begin{aligned} g({f(x)})&=({2x+3})^2-3({2x+3})+1\\ \\ &=4x^2+12x+9-6x-9+1\\ \\ &=4x^2+6x+1\\ \\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $g(f(x))=4x^2+6x+1$